1. Field of the Invention
This invention relates to a frequency mixing circuit and more particularly, to a frequency mixing circuit formed on a bipolar integrated circuit.
2. Description of the Related Art
A conventional frequency mixing circuit is shown in FIG. 1, which comprises a differential amplifier formed of transistors Q11 and Q12 and a transistor Q13 serving to act as a current source for driving the differential amplifier. A load resistance RL is connected to the collector of the transistor Q12. A first frequency signal (voltage; VIN) is superposed on a reference voltage VF of the current source formed of the transistor Q13 and applied thereto, and a second frequency signal (voltage; VLO) is applied to the input terminals pair of the differential amplifier. The output of this circuit is taken out from one end of the load resistance RL.
The operation of this circuit will be explained below.
The junction diode (base-emitter junction) forming a transistor generally has the current characteristic as shown below, EQU IE=IS.multidot.exp(q.multidot.VBE/kT)-1 (1)
where
IE is the emitter current, PA1 IS is the saturation current, PA1 q is the unit electron charge, PA1 VBE is the base-to-emitter voltage, PA1 k is Boltzmann's constant, and PA1 T is absolute temperature.
Here, if VT=kT/q, then VBE&gt;&gt;VT in general. As a result, if exp(VBE/VT)&gt;&gt;1 in the equation (1), the emitter current IE is approximated as follows; EQU IE.apprxeq.IS.multidot.exp(VBE/VT) (2)
In this case, the collector current IC13 of the transistor Q13 serving to act as the current source can be expressed as follows; EQU IC13=IS13.multidot.exp{(VF+VIN)/VT} (3)
Hence, if the constant current IO is expressed as EQU IO=IS13.multidot.exp(VF/VT) (4),
from the equation (3), the collector current IC13 is expressed as follows; EQU IC13=IO.multidot.exp(VIN/VT) (5)
The differential input voltage VL0 of the second frequency signal becomes equal to the difference of the base-to-emitter voltage VBE11 of the transistor Q11 and the base-to-emitter voltage VBE12 of the transistor Q12, or EQU VBE11-VBE12=VLO (6)
Then, suppose that the base-to-emitter voltages VBE11 and VBE12 are respectively expressed as the following equations (7) and (8) and suppose that IS11 and IS12 in the equations (7) and (8) are equal to each other as shown in the following equation (9), as EQU VBE11=VT.multidot.ln(IC11/IS11) (7) EQU VBE12=VT.multidot.ln(IC12/IS12) (8) EQU IS11=IS12 (9)
Then, the differential input voltage VLO shown in the equation (6) can be expressed as follows; EQU VT.multidot.ln(IC11/IC12)=VLO (10)
On the other hand, if the DC common-base current gain factor of the transistors is expressed as .alpha.F, the sum of the collector current IC11 and collector current IC12 can be expressed as follows: EQU IC11+IC12=.alpha.F.multidot.IC13 (11)
As a result, from the equations (10) and (11), the collector currents IC11 and IC12 can be respectively obtained as follows; ##EQU1##
Accordingly, the differential current .DELTA.13 of the collector currents IC11 and IC12 can be expressed as follows; ##EQU2## where tanh X and exp X (X&lt;&lt;1) can be respectively expanded as follows; EQU tanh x=x-(1/3).multidot.x.sup.3 + . . . (15) EQU exp x=1+(x/1!)+(x.sup.2 /2!)+ . . . (16)
Then, if the equation (14) is expressed using the equations (15) and (16), the following can be obtained: ##EQU3##
As seen from the equation (17), the differential current .DELTA.I3 includes the term of the product (VIN.multidot.VLO) of the first frequency input voltage VIN and the second frequency input voltage VLO. Here, suppose that the input voltages VIN and VLO are respectively expressed as; EQU VIN=.vertline.VIN.vertline..multidot.COS 2.pi..multidot.fIN.multidot.t(18) EQU VLO=.vertline.VIN.vertline..multidot.COS 2.pi..multidot.fLO.multidot.t(19)
Then, the product (VIN.multidot.VLO) can be expressed as follows: EQU VIN.multidot.VLO=(1/2).vertline.VIN.vertline..vertline.VLO.vertline..times. ]COS {2.pi.(fIN+fLO)t}+COS {2.pi.(fIN-fLO)t}] (20)
Hence, the components of the sum (fIN+fLO) and difference .vertline.fIN-fLO.vertline. of the first and second frequencies fIN and fLO can be obtained.
As seen from the equation (20), the factor specifying the frequency characteristic depends mainly on the frequency characteristic (transition frequency; fT) of the transistors used, so that it can be found that the circuit in FIG. 1 is the frequency mixing circuit having a good high frequency characteristic.
Since the collector currents IC11 and IC12 are differential currents, they can be expressed as follows: EQU IC11=(1/2)(.alpha.F.multidot.IO+.DELTA.I3) (21) EQU IC12=(1/2)(.alpha.F.multidot.IO-.DELTA.I3) (22)
As seen from these equations (21) and (22), the collector currents IC11 and IC12 respectively include the terms of {.+-.(1/2).multidot..DELTA.I3}. As a result, if the collector current IC11 or IC12 is converted into a voltage, the output voltage including the components of the sum (fIN+fLO) and difference .vertline.fIN-fLO.vertline. of the first and second frequencies fIN and fLO can be obtained.
In the circuit shown in FIG. 1, the collector current IC12 is converted into the voltage through the load resistance RL.
Another example of a conventional frequency mixing circuit is shown in FIG. 2, in which the first frequency signal (voltage; VIN) is applied to a first input terminal of an analog multiplier 31 such as the Gilbert multiplier or the like and the second frequency signal (voltage; VLO) is applied to a second input terminal thereof.
In FIG. 2, an output voltage VO can be expressed as follows; EQU VO=A.multidot.VIN.multidot.VLO (23)
where A is a constant having a dimension of inverse voltage.
By substituting the equations (18) and (19) into the equation (23), similar to the equation (20), the output voltage VO can be obtained as follows: EQU VO=(A/2).vertline.VIN.vertline..vertline.VLO.vertline..times.[COS }2.pi.(fiN+fLO)t}+COS {2.pi.(fiN-fLO)t}] (24)
As a result, it can be found that the circuit using the analog multiplier 31 shown in FIG. 2 is a frequency mixing circuit similar to the circuit shown in FIG. 1.
In this case, however, with the conventional frequency mixing circuit shown in FIG. 1, there arises such a problem that in the transistor Q13 as the current source, it is difficult to superpose the signal voltage to the reference voltage for applying thereto. In addition, with another conventional frequency mixing circuit shown in FIG. 2, because the number of transistors to be used in the multiplier 31 is large, the noise factor (NF) is degraded, arising a problem that the circuit current is required to be increased in order to obtain a good high frequency characteristic.